Question

given the triangle below, what is the length of the hypotenuse? 2 cm 4 cm a 20 cm b 12 cm c $sqrt{12}$ cm d $sqrt{20}$ cm

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Here \(a = 4\) cm and \(b = 2\) cm. So \(c^{2}=4^{2}+2^{2}\).

Step2: Calculate \(a^{2}+b^{2}\)

\(4^{2}+2^{2}=16 + 4=20\). So \(c^{2}=20\).

Step3: Solve for \(c\)

Taking the square root of both sides, \(c=\sqrt{20}\) cm.

Answer:

D. \(\sqrt{20}\) cm